Question

An astronaut landed on a far away planet that has a sea of water. To determine the gravitational acceleration on the planet's surface, the astronaut lowered a pressure gauge into the sea to a depth of 12.3 m. If the gauge pressure is measured to be 1.1 atm, what is the gravitational acceleration on the planet's surface? Use 1000 kg/m3 as the mass density of water.

Answer 1

To solve this problem it is necessary to apply the concepts related to hydrostatic pressure or pressure due to a fluid.

Mathematically this pressure is given under the formula

$P_h = \rho g h$

Where,

$\rho$ = Density

h = Height

g = Gravitational acceleration

Rearranging in terms of g

$g = \frac{P_h}{\rho h}$

our values are given as

$P_h = 1.1 atm (\frac{101325Pa}{1atm}) = 111457.5Pa$

$\rho = 1000kg/m^3$

$h = 12.3m$

Replacing we have

$g = \frac{111457.5}{(1000)(12.3)}$

$g = 9.061m/s^2$

Therefore the gravitational acceleration on the planet's surface is $9.061m/s^2$ (Almost the gravity of the Earth)